I study climate policy choices for a 'policy bloc' of fuel-importers, when a 'fringe' of other fuel importers have no climate policy, fuel exporters consume no fossil fuels, and importers produce no such fuels. The policy bloc and exporter blocs act strategically in fossil fuel markets. When the policy bloc sets a carbon tax, the fuel import price set by the exporter is reduced, and more so when the policy bloc is larger. The carbon tax then serves to extract the exporter's rent. The fringe also gains from reduced fuel import prices, and gains more when the policy bloc is larger. When the policy bloc sets an emissions cap, fuel demand becomes less price elastic. In response, a monopolistic exporter sets the fuel export price higher than under a tax, which hurts both the policy bloc and the fringe. This effect can be stronger when the policy bloc is larger, so that the fringe loses when the policy bloc is larger, opposite to the tax policy case. Overall, a cap is inferior to a tax for fossil fuel importers, both those that implement a climate policy, and those that do not.